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TITLE: Estimation of a semiparametric mixture of regressions model
SPEAKER: Professor Pierre VANDEKERKHOVE
Maitre de conférences at the department of Analysis and Applied Mathematics of the University Paris-Est Marne-la-Vallée, and invited professor at the department of Materials Science and Engineering, Georgia Institute of Technology
ABSTRACT:
We introduce in this paper a new mixture of regressions model which is a generalization of the semiparametric two-component mixture model studied in Bordes et al. (2006) and Bordes and Vandekerkhove (2010). Namely we consider a two-component mixture of regressions model in which one component is entirely known while the Euclidean parameters and the error distribution of the other component, the mixing ratio, and the distribution of the design data are unknown. Our model is said to be semiparametric in the sense that the probability density function (pdf) of the error involved in the unknown regression model cannot be modeled adequately by using a parametric density family. When the pdf's of the errors involved in each regression model are supposed to be zero-symmetric, we propose an estimator of the various (Euclidean and functional) parameters of the model, and prove under mild conditions its convergence. We prove in particular that, under semiparametric technical conditions all satisfied in the Gaussian case, the Euclidean part of the model is estimated at the rate $o_{a.s}(n^{-1/4+\gamma})$, $\gamma>0$. Finally the implementation and numerical performances of our method are discussed using several simulated datasets and one real microarray dataset (ChipMIX model).
Professor Pierre VANDEKERKHOVE received his Ph.D. in 1998 in Biostatistics at the university Montpellier II, France. His field of research includes Statistics and Applied probability focusing on missing data models and stochastic algorithms, Markov Chain Monte Carlo algorithms.
Contact: "VANDEKERKHOVE Pierre" <Pierre.Vandekerkhove@univ-mlv.fr>
